arXiv subjects

François Renard

Publications and source records attributed to François Renard.

At least 19 recordsLinked to original sources

arXiv2026

How pore-scale disorder controls fluid stretching in two-dimensional porous media

Fluid stretching in porous media governs the mixing of reactants, contaminants, and nutrients, yet how the solid microstructure controls the stretching statistics remains poorly understood. We investigate how porous-medium heterogeneity controls stretching using (i) particle-tracking velocimetry experiments in 3D-printed millifluidic cells, (ii) numerical simulations of solute-plume deformation in the measured flow fields, and (iii) analytical calculations of fluid stretching. The cells contain arrays of cylindrical rods with systematically-varying disorder levels, from ordered to random. Velocity and shear-rate measurements reveal that fluid deformation is strongly localized near solid boundaries for all disorder levels, suggesting that near-wall flow is the main driver of stretching. The mean stretching grows linearly in time for ordered media and quadratically for disordered media, while the stretching distributions are approximately log-normal. We analytically describe the stretching produced by flow around an isolated cylinder and embed this description in a random-walk model that reproduces the observed stretching statistics in random media. These results provide the first quantitative connection between porous-medium structure and fluid-stretching statistics, revealing the extent to which disordered media accelerate mixing relative to ordered media and enabling progress beyond the common mean-field description of stretching in two-dimensional media as a simple shear flow.

physics.flu-dyn↗

arXiv2026

A phase-field modeling approach to sea-ice fracturing

The thin ice that covers the polar oceans is a complex geomaterial that is constantly stressed and fractured by winds and ocean currents. In the central Arctic, this forcing produces deformations in the form of shear bands, within which individual ice plates detach, locally generating a granular medium. Capturing this transition from a continuous to a granular sea-ice cover has implications for the adequate representation of the mechanical and dynamical behavior of sea-ice in regional and large-scale models used for operational and climate prediction purposes. Our work investigates the feasibility of a phase-field approach to capture this granularization processes and focuses on fracture propagation in the material. The model combines a double-well free-energy formulation with an overdamped displacement response. The governing equations are solved using a spectral method in Fourier space. The implementation accounts for body forces, representative of the main forcings on sea-ice, and remains computationally tractable despite the highly nonlinear character of the double-well energy formulation. We first validate the framework against a benchmark problem: the opening of an inclusion embedded into an elastic matrix under tensile loading. Then, additional simple shear configurations are investigated: an inclusion solicited under plane shear and a cylindrical Couette experiment, for which the analytical solution of the displacement field is known. The resulting fracture patterns and displacement fields demonstrate that our phase-field framework captures key features of tensile and shear fracture propagation, including the linear scaling between crack speed and applied load predicted by the Griffith's theory.

physics.class-ph↗

arXiv2026

Energy dissipation at the atomic scale explains how fracture energy depends on crack velocity in silica glass

The fracture energy of brittle materials rises with crack velocity, and this effect is typically attributed to surface roughening from path instabilities. Here we show, using molecular dynamics simulations of silica glass with a first-principles machine learned interatomic potential, that the structural fracture energy rises by up to 33 % already below the branching threshold, showing that fracture energy is not a constant material property. This rise in fracture energy is roughly equally partitioned between an increase in the intrinsic surface energy density and nanoscale roughening that increases the real fracture surface area. Results demonstrate that dynamic fracture in silica glass increases the fracture energy not merely by creating more apparent surface, but also by creating a fundamentally different surface at the nanoscale.

cond-mat.mtrl-sci↗

arXiv2026

Dynamic multiphase flow triggers chaotic mixing in porous media

Solute mixing plays a pivotal role in a broad spectrum of chemical and biological processes across natural and engineered porous media. However, current understanding of mixing dynamics remains largely constrained to steady flows in fully or partially water-saturated environments. Multiphase flow systems are generally unsteady, with moving fluid interfaces and flow paths that change in time. Despite the widespread occurrence of dynamic multiphase flows, their impacts on solute mixing are largely unknown. Here, we use experiments and numerical simulations to investigate the effect of dynamic two-phase flow on the stretching and folding of fluid elements, a fundamental mechanism driving solute mixing and reactions in porous media. We find that dynamic two-phase flows induce chaotic mixing, characterized by exponential stretching of fluid elements, leading to strongly enhanced mixing compared to steady single phase flows. By extensive numerical multiphase flow simulations, we establish dynamic steady states where we reliably measure the mean fluid stretching rate as a function of flow rate. We show that stretching is maximized at an optimum flow rate which balances fluid shear deformation against the frequency of flow reorientation by the intermittent motion of the fluid interface. The findings are rationalized by a mechanistic model linking basic multiphase flow characteristics to the stretching rate, opening new perspectives to understand and control mixing and reactions in a wide range of multiphase flow systems.

physics.flu-dyn↗

arXiv2025

Unveiling the role of seepage forces in the acceleration of landslides creep

In the context of global climate change, geological materials are increasingly destabilized by water flow and infiltration. We study the creeping dynamics of a densely monitored landslide in Western Norway to decipher the role of fluid flow in destabilizing this landslide. In Åknes, approximately 50 million cubic meter of rock mass continuously creeps over a shear zone made of rock fragments, with seasonal accelerations that strongly correlate with rainfall. In this natural laboratory for fluid-induced frictional creep, unprecedented monitoring equipment reveals low fluid pressure across the shear zone, thereby challenging the dominant theory of fluid-driven instability in landslides. Here, we show that a generic micromechanical model can disentangle the effects of fluid flow from those of fluid pressure, and demonstrate that seepage forces applied by channelized flow along the shear zone are the main driver of creep accelerations. We conclude by discussing the significance of seepage forces, the implications for hazard mitigation and the broader applicability of our model to various geological contexts governed by friction across saturated shear zones.

physics.geo-ph↗

arXiv2021

A minimal model for the onset of slip pulses in frictional rupture

We present a minimal one-dimensional model for the transition from crack-like to pulse-like propagation of frictional rupture. In its non-dimensional form, the model depends on only two free parameters: the non-dimensional pre-stress and an elasticity ratio that accounts for the finite height of the system. The model contains stable slip pulse solutions for slip boundary conditions, and unstable slip pulse solutions for stress boundary conditions. Results demonstrate that the existence of pulse-like ruptures requires only elastic relaxation and redistribution of initial pre-stress. The novelty of our findings is that pulse-like propagation along frictional interfaces is a generic elastic feature, whose existence is not sensitive to particular rate- or slip-dependencies of dynamic friction.

physics.geo-ph↗

arXiv2021

Frictional anisotropy of 3D-printed fault surfaces

The surface morphology of faults controls the spatial anisotropy of their frictional properties, and hence their mechanical stability. Such anisotropy is only rarely studied in seismology models of fault slip, although it might be paramount to understand the seismic rupture in particular areas, notably where slip occurs in a direction different from that of the main striations of the fault. To quantify how the anisotropy of fault surfaces affects the friction coefficient during sliding, we sheared synthetic fault planes made of plaster of Paris. These fault planes were produced by 3D-printing real striated fault surfaces whose 3D roughness was measured in the field at spatial scales from millimeters to meters. Here, we show how the 3D-printing technology can help for the study of frictional slip. Results show that fault anisotropy controls the coefficient of static friction, with the friction coefficient along the striations being three to four times smaller than the friction coefficient along the direction perpendicular to the striations. This is true both at the meter and the millimeter scales. The anisotropy in friction and the average coefficient of static friction are also shown to decrease with the normal stress applied to the faults, as a result of the increased surface wear under increased loading.

physics.geo-ph↗

arXiv2019

A minimal model for slow, sub-Rayleigh, super-shear and unsteady rupture propagation along homogeneously loaded frictional interfaces

In nature and experiments, a large variety of rupture speeds and front modes along frictional interfaces are observed. Here, we introduce a minimal model for the rupture of homogeneously loaded interfaces with velocity strengthening dynamic friction, containing only two dimensionless parameters; $\bar τ$ which governs the prestress, and $\bar α$ which is set by the dynamic viscosity. This model contains a large variety of front types, including slow fronts, sub-Rayleigh fronts, super-shear fronts, slip pulses, cracks, arresting fronts and fronts that alternate between arresting and propagating phases. Our results indicate that this wide range of front types is an inherent property of frictional systems with velocity strengthening branches.

physics.comp-ph↗

arXiv2019

Self-similar distributions of fluid velocity and stress heterogeneity in a dissolving porous limestone

In a porous rock, the spatial distribution of the pore space induces a strong heterogeneity in fluid flow rates and in the stress distribution in the rock mass. If the rock microstructure evolves through time, for example by dissolution, fluid flow and stress will evolve accordingly. Here, we consider a core sample of porous limestone that has undergone several steps of dissolution. Based on 3D X-ray tomography scans, we calculate numerically the coupled system of fluid flow in the pore space and stress in the solid. We determine how the flow field affects the stress distribution both at the pore wall surface and in the bulk of the solid matrix. We show that, during dissolution, the heterogeneous stress evolves in a self-similar manner as the porosity is increased. Conversely, the fluid velocity shows a stretched exponential distribution. The scalings of these common master distributions offer a unified description of the porosity evolution, pore flow, and the heterogeneity in stress for a rock with evolving microstructure. Moreover, the probability density functions of stress invariants (mechanical pressure or von Mises stress) display heavy tails towards large stresses. If these results can be extended to other kinds of rocks, they provide an additional explanation of the sensitivity to failure of porous rocks under slight changes of stress.

physics.geo-ph↗

arXiv2008

Characterization of Fault Roughness at Various Scales: Implications of Three-Dimensional High Resolution Topography Measurements

Accurate description of the topography of active faults surfaces represents an important geophysical issue because this topography is strongly related to the stress distribution along fault planes, and therefore to processes implicated in earthquake nucleation, propagation, and arrest. With the recent development of Light Detection And Ranging (LIDAR) apparatus, it is now possible to measure accurately the 3D topography of rough surfaces with a comparable resolution in all directions, both at field and laboratory scales. In the present study, we have investigated the scaling properties including possible anisotropy properties of several outcrops of two natural fault surfaces (Vuache strike-slip fault, France, and Magnola normal fault, Italy) in limestones.

physics.geo-ph↗

arXiv2008

Evolution of seismic signals and slip patterns along subduction zones: insights from a friction lab scale experiment

Continuous GPS and broadband seismic monitoring have revealed a variety of disparate slip patterns especially in shallow dipping subduction zones, among which regular earthquakes, slow slip events and silent quakes1,2. Slow slip events are sometimes accompanied by Non Volcanic Tremors (NVT), which origin remains unclear3, either related to fluid migration or to friction. The present understanding of the whole menagerie of slip patterns is based upon numerical simulations imposing ad hoc values of the rate and state parameters a and b4-6 derived from the temperature dependence of a and b of a wet granite gouge7. Here we investigate the influence of the cumulative slip on the frictional and acoustic patterns of a lab scale subduction zone. Shallow loud earthquakes (stick-slip events), medium depth slow, deeper silent quakes (smooth sliding oscillations) and deepest steady-state creep (continuous sliding) are reproduced by the ageing of contact interface with cumulative displacement8. The Acoustic Emission evolves with cumulative displacement and interface ageing, following a trend from strong impulsive events, similar to earthquake seismic signals, to a collection of smaller amplitude and longer duration signals, similar to Non Volcanic Tremors. NVT emerge as the recollection of the local unstable behaviour of the contact interface globally evolving towards the stable sliding regime.

physics.geo-ph↗

arXiv2008

Single-contact pressure solution creep on calcite monocrystals

Pressure solution creep rates and interface structures have been measured by two methods on calcite single crystals. In the first kind of experiments, calcite monocrystals were indented at 40 degrees C for six weeks using ceramic indenters under stresses in the 50-200 MPa range in a saturated solution of calcite and in a calcite-saturated aqueous solution of NH4Cl. The deformation (depth of the hole below the indenter) is measured ex-situ at the end of the experiment. In the second type of experiment, calcite monocrystals were indented by spherical glass indenters for 200 hours under stresses in the 0-100 MPa range at room temperature in a saturated aqueous solution of calcite. The displacement of the indenter was continuously recorded using a specially constructed differential dilatometer. The experiments conducted in a calcite-saturated aqueous solution of NH4Cl show an enhanced indentation rate owing to the fairly high solubility of calcite in this solution. In contrast, the experiments conducted in a calcite-saturated aqueous solution show moderate indentation rate and the dry control experiments did not show any measurable deformation. The rate of calcite indentation is found to be inversely proportional to the indenter diameter, thus indicating that the process is diffusion-controlled. The microcracks in the dissolution region under the indenter dramatically enhance the rate of calcite indentation by a significant reduction of the distance of solute transport in the trapped fluid phase. This result indicates that care should be taken in extrapolating the kinetic data of pressure solution creep from one mineral to another.

physics.geo-ph↗

arXiv2008

Growth of stylolite teeth patterns depends on normal stress and finite compaction

Stylolites are spectacular rough dissolution surfaces that are found in many rock types. Despite many studies, their genesis is still debated, particularly the time scales of their formation and the relationship between this time and their morphology. We developed a new discrete simulation technique to explore the dynamic growth of the stylolite roughness, starting from an initially flat dissolution surface. We demonstrate that the typical steep stylolite teeth geometry can accurately be modelled and reproduce natural patterns. The growth of the roughness takes place in two successive time regimes: i) an initial non-linear increase in roughness amplitude that follows a power-law in time up to ii) a critical time where the roughness amplitude saturates and stays constant.

physics.geo-ph↗

arXiv2008

Albite feldspar dissolution kinetics as a function of the Gibbs free energy at high pCO_2

We are currently measuring the dissolution kinetics of albite feldspar at 100 deg C in the presence of high levels of dissolved CO_2 (pCO_2 = 9 MPa) as a function of the saturation state of the feldspar (Gibbs free energy of reaction, ΔG). The experiments are conducted using a flow through reactor, thereby allowing the dissolution reactions to occur at a fixed pH and at constant, but variable saturation states. Preliminary results indicate that at far-from-equilibrium conditions, the dissolution kinetics of albite are defined by a rate plateau, with R \approx 5.0 x 10^{-10} mol m^{-2} s^{-1} at -70 < ΔG < -40 kJ mol^{-1}. At ΔG > -40 kJ mol^{-1}, the rates decrease sharply, revealing a strong inverse relation between the dissolution rate and free energy. Based on the experiments carried out to date, the dissolution rate-free energy data correspond to a highly non-linear and sigmoidal relation, in accord with recent studies.

physics.geo-ph↗

arXiv2008

Rhombohedral calcite precipitation from CO2-H2O-Ca(OH)2 slurry under supercritical and gas CO2 media

The formation of solid calcium carbonate (CaCO3) from aqueous solutions or slurries containing calcium and carbon dioxide (CO2) is a complex process of considerable importance in the ecological, geochemical and biological areas. Moreover, the demand for powdered CaCO3 has increased considerably recently in various fields of industry. The aim of this study was therefore to synthesize fine particles of calcite with controlled morphology by hydrothermal carbonation of calcium hydroxide at high CO2 pressure (initial PCO2=55 bar) and at moderate and high temperature (30 and 90 degrees C). The morphology of precipitated particles was identified by transmission electron microscopy (TEM/EDS) and scanning electron microscopy (SEM/EDS). In addition, an X-ray diffraction analysis was performed to investigate the carbonation efficiency and purity of the solid product. Carbonation of dispersed calcium hydroxide in the presence of supercritical (PT=90 bar, T=90 degrees C) or gaseous (PT=55 bar, T=30 degrees C) CO2 led to the precipitation of sub-micrometric isolated particles (<1$μ$m) and micrometric agglomerates (<5$μ$m) of calcite. For this study, the carbonation efficiency (Ca(OH)2-CaCO3 conversion) was not significantly affected by PT conditions after 24 h of reaction. In contrast, the initial rate of calcium carbonate precipitation increased from 4.3 mol/h in the "90bar-90 degrees C" system to 15.9 mol/h in the "55bar-30 degrees C" system. The use of high CO2 pressure may therefore be desirable for increasing the production rate of CaCO3, carbonation efficiency and purity, to approximately 48 kg/m3h, 95% and 96.3%, respectively in this study. The dissipated heat for this exothermic reaction was estimated by calorimetry to be -32 kJ/mol in the "90bar-90 degrees C" system and -42 kJ/mol in the "55bar-30 degrees C" system.

physics.geo-ph↗

arXiv2008

Variety of stylolites morphologies and statistical characterization of the amount of heterogeneities in the rock

The surface roughness of several stylolites in limestones was measured using high resolution laser profilometry. The 1D signals obtained were statistically analyzed to determine the scaling behavior and calculate a roughness exponent, also called Hurst exponent. Statistical methods based on the characterization of a single Hurst exponent imply strong assumptions on the mathematical characteristics of the signal: the derivative of the signal (or local increments) should be stationary and have finite variance. The analysis of the measured stylolites show that these properties are not always verified simultaneously. The stylolite profiles show persistence and jumps and several stylolites are not regular, with alternating regular and irregular portions. A new statistical method is proposed here, based on a non-stationary but Gaussian model, to estimate the roughness of the profiles and quantify the heterogeneity of stylolites. This statistical method is based on two parameters: the local roughness (H) which describes the local amplitude of the stylolite, and the amount of irregularities on the signal (μ), which can be linked to the heterogeneities initially present in the rock before the stylolite formed. Using this technique, a classification of the stylolites in two families is proposed: those for which the morphology is homogeneous everywhere and those with alternating regular and irregular portions.

physics.geo-ph↗

arXiv2008

Influence of time, temperature, confining pressure and fluid content on the experimental compaction of spherical grains

Theoretical models of compaction processes, such as for example intergranular pressure-solution (IPS), focus on deformation occurring at the contacts between spherical grains that constitute an aggregate. In order to investigate the applicability of such models, and to quantify the deformation of particles within an aggregate, isostatic experiments were performed in cold-sealed vessels on glass sphere aggregates at 200 MPa confining pressure and 350 degrees C with varying amounts of fluid.

physics.geo-ph↗

arXiv2008

Thermal imaging on simulated faults during frictional sliding

Heating during frictional sliding is a major component of the energy budget of earthquakes and represents a potential weakening mechanism. It is therefore important to investigate how heat dissipates during sliding on simulated faults. We present results from laboratory friction experiments where a halite (NaCl) slider held under constant load is dragged across a coarse substrate. Surface evolution and frictional resistance are recorded. Heat emission at the sliding surface is monitored using an infra-red camera. We demonstrate a link between plastic deformations of halite and enhanced heating characterized by transient localized heat spots. When sand 'gouge' is added to the interface, heating is more diffuse. Importantly, when strong asperities concentrate deformation, significantly more heat is produced locally. In natural faults such regions could be nucleation patches for melt production and hence potentially initiate weakening during earthquakes at much smaller sliding velocities or shear stress than previously thought.

physics.geo-ph↗